Question

De Broglie wavelength of a particle B is double to that of particle Aand mass of particle A is thrice the mass of particle b , find the ratio of velocity of particle A to B

Answer 1

Given :

Mass of particle A = 3 * ( Mass of particle B )

De Broglie wavelength of particle B = 2 * ( De Broglie wavelength of particle B )

To find :

The ratio of the velocity of particles A and B .

Solution :

Let Va and Vb be velocities of the particles A and B respectively .

Let Mb be mass of particle B and Ma be the mass of particle A .

Then ,  

Ma = 3 Mb

Let the De Broglie wavelength of particle A be λa and the De Broglie wavelength of particle B be λb .

Then ,

λb = 2 * λa

De Broglie wavelength , λ = h / mv            

For particle A , λa = h / Ma * Va         .....(i)

For particle B , λb = h / Mb * Vb         .....(ii)

dividind (ii) by (i) ,

( Ma * Va ) / ( Mb * Vb ) = λb / λa

Va / Vb = 2 : 3

The ratio of the velocity of particles A and B is 2 : 3 .